The anatomy of Leo I: how tidal tails affect the kinematics

We model the recently published kinematic data set for Leo I dSph galaxy by fitting the solutions of the Jeans equations to the velocity dispersion and kurtosis profiles measured from the data. We demonstrate that when the sample is cleaned of interlopers the data are consistent with the assumption that mass follows light and isotropic stellar orbits with no need for an extended dark matter halo. Our interloper removal scheme does not clean the data of contamination completely, as demonstrated by the rotation curve of Leo I. When moving away from the centre of the dwarf, the rotation appears to be reversed. We interpret this behaviour using the results of an N-body simulation of a dwarf galaxy possessing some intrinsic rotation, orbiting in the Milky Way potential and show that it can be reproduced if the galaxy is viewed almost along the tidal tails so that the leading (background) tail contaminates the western part of Leo I while the trailing (foreground) tail the eastern one. We show that this configuration leads to a symmetric and Gaussian distribution of line-of-sight velocities. The simulation is also applied to test our modelling method on mock data sets. We demonstrate that when the data are cleaned of interlopers and the fourth velocity moment is used the true parameters of the dwarf are typically within 1 \sigma errors of the best-fitting parameters. Restricting the fitting to the inner part of Leo I our best estimate for the anisotropy is \beta = -0.2^{+0.3}_{-0.4} and the total mass M = (4.5 +/- 0.7) x 10^7 M_sun. The mass-to-light ratio including the errors in mass, brightness and distance is M/L_V = 8.2 +/- 4.5 solar units.Comment: 10 pages, 10 figures, revised version accepted for publication in MNRA

Tidal stirring of Milky Way satellites: a simple picture with the integrated tidal force

Most of dwarf spheroidal galaxies in the Local Group were probably formed via environmental processes like the tidal interaction with the Milky Way. We study this process via N-body simulations of dwarf galaxies evolving on seven different orbits around the Galaxy. The dwarf galaxy is initially composed of a rotating stellar disk and a dark matter halo. Due to the action of tidal forces it loses mass and the disk gradually transforms into a spheroid while stellar motions become increasingly random. We measure the characteristic scale-length of the dwarf, its maximum circular velocity, mass, shape and kinematics as a function of the integrated tidal force along the orbit. The final properties of the evolved dwarfs are remarkably similar if the total tidal force they experienced was the same, independently of the actual size and eccentricity of the orbit.Comment: 5 pages, 2 figures, contribution to the proceedings of JENAM 2010 in Lisbon, Symposium 2 "Environment and the formation of galaxies: 30 years later", comments welcom

The mass and anisotropy profiles of galaxy clusters from the projected phase space density: testing the method on simulated data

We present a new method of constraining the mass and velocity anisotropy profiles of galaxy clusters from kinematic data. The method is based on a model of the phase space density which allows the anisotropy to vary with radius between two asymptotic values. The characteristic scale of transition between these asymptotes is fixed and tuned to a typical anisotropy profile resulting from cosmological simulations. The model is parametrized by two values of anisotropy, at the centre of the cluster and at infinity, and two parameters of the NFW density profile, the scale radius and the scale mass. In order to test the performance of the method in reconstructing the true cluster parameters we analyze mock kinematic data for 20 relaxed galaxy clusters generated from a cosmological simulation of the standard LCDM model. We use Bayesian methods of inference and the analysis is carried out following the Markov Chain Monte Carlo approach. The parameters of the mass profile are reproduced quite well, but we note that the mass is typically underestimated by 15 percent, probably due to the presence of small velocity substructures. The constraints on the anisotropy profile for a single cluster are in general barely conclusive. Although the central asymptotic value is determined accurately, the outer one is subject to significant systematic errors caused by substructures at large clustercentric distance. The anisotropy profile is much better constrained if one performs joint analysis of at least a few clusters. In this case it is possible to reproduce the radial variation of the anisotropy over two decades in radius inside the virial sphere.Comment: 11 pages, 10 figures, accepted for publication in MNRA

How to make an ultra-faint dwarf spheroidal galaxy: tidal stirring of disky dwarfs with shallow dark matter density profiles

In recent years the Sloan Digital Sky Survey has unraveled a new population of ultra-faint dwarf galaxies (UFDs) in the vicinity of the Milky Way (MW) whose origin remains a puzzle. Using a suite of collisionless N-body simulations, we investigate the formation of UFDs in the context of the tidal stirring model for the formation of dwarf spheroidal galaxies in the Local Group (LG). Our simulations are designed to reproduce the tidal interactions between MW-sized host galaxies and rotationally supported dwarfs embedded in 10^9 M_sun dark matter (DM) halos. We explore a variety of inner density slopes \rho \propto r^{-\alpha} for the dwarf DM halos, ranging from core-like (\alpha = 0.2) to cuspy (\alpha = 1), and different dwarf orbital configurations. Our experiments demonstrate that UFDs can be produced via tidal stirring of disky dwarfs on relatively tight orbits, consistent with a redshift of accretion by the host galaxy of z \sim 1, and with intermediate values for the halo inner density slopes (\rho \propto r^{-0.6}). The inferred slopes are in excellent agreement with those resulting from both the modeling of the rotation curves of dwarf galaxies and recent cosmological simulations of dwarf galaxy formation. Comparing the properties of observed UFDs with those of their simulated counterparts, we find remarkable similarities in terms of basic observational parameters. We conclude that tidal stirring of rotationally supported dwarfs represents a viable mechanism for the formation of UFDs in the LG environment.Comment: 6 pages, 4 figures, revised version accepted for publication in ApJ Letter

Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy

We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalised formula based upon the results of cosmological N-body simulations. Its inner slope (cuspy or flat), concentration, and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line-of-sight velocity dispersion alone does not allow to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3% of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope $\alpha$ and concentration $c$: the best-fitting profiles have the two parameters related with $c=19 - 9.6 \alpha$. Our best-fitting NFW profile has concentration $c=9$, which is 50% higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of $2.9 h_{70}^{-1}$ Mpc is 1.4 \times 10^{15} h_{70}^{-1} M_{\sun} (with 30% accuracy), 85% of which is dark. At this distance from the cluster centre, the mass-to-light ratio in the blue band is $351 h_{70}$ solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass-to-light ratio and baryonic fraction of the Universe, with $\Omega_0=0.29 \pm 0.1$.Comment: 13 pages, 10 figures, revised version accepted by MNRAS with discussion on substructure and equilibrium of elliptical galaxies adde

The distribution function of dark matter in massive haloes

We study the distribution function (DF) of dark matter particles in haloes of mass range 10^{14}--10^{15}\Msun. In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard \LambdaCDM model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L, a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form f_{E}(E)[1+L^{2}/(2L_{0}^{2})]^{-\beta_{\infty}+\beta_{0}}L^{-2\beta_{0}}. This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (\beta_{0} and \beta_{\infty}) and the scale of transition between them (L_{0}). The energy part f_{E}(E) is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase space density Q=\rho(r)/\sigma^{3}(r).Comment: 16 pages, 12 figures, final version accepted for publication in MNRA

Hubble Space Telescope survey of the Perseus Cluster - I: The structure and dark matter content of cluster dwarf spheroidals

We present the results of a Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) study of dwarf galaxies in the core of the rich nearby Perseus Cluster, down to M_V=-12. We identify 29 dwarfs as cluster members, 17 of which are previously unstudied. All the dwarfs we examine are remarkably smooth in appearance, and lack internal features. Based on these observations, and the sizes of these dwarfs, we argue that some of the dwarfs in our sample must have a large dark matter content to prevent disruption by the cluster potential. We derive a new method, independent of kinematics, for measuring the dark matter content of dEs, based on the radius of the dwarf, the projected distance of the dwarf from the cluster centre, and the total mass of the cluster interior to it. We find that the mass-to-light ratios of these dwarfs are comparable to those of the Local Group dSphs, ranging between 1 and 120.Comment: accepted for publication by MNRA

Galaxies with kinematically distinct cores in Illustris

The growing amount of integral-field spectroscopic data creates an increased demand for understanding kinematic peculiarities that carry valuable information about the evolution of the host galaxies. For kinematically distinct cores (KDCs), a number of formation mechanisms have been proposed, but it is still unclear which of them commonly occur in the Universe. We aim to address the KDC formation in the cosmological context. We used the publicly available data of the large-scale hydrodynamic cosmological simulation Illustris. We identify 134 KDCs, study their properties, and follow their evolution back in time. Examples of four galaxies hosting KDCs are presented and described in detail. The masses of the KDC hosts follow the general distribution of the Illustris galaxies, with a possible slight preference towards massive galaxies. KDCs can be long-lived features, with their formation epochs roughly uniformly distributed in look-back times 0-11.4 Gyr, and they can survive even major or multiple subsequent mergers. There is no single channel of KDC formation, but mergers seem to be the formation mechanism for about 60% of KDCs with a significant preference for major mergers and with the percentage being higher among massive hosts. Other KDCs formed during a pericentric passage or flyby of another galaxy, by precession of a previously formed rapidly rotating core, or without an obvious external cause. The mean mass-weighted stellar age inside the KDC radius is either about the same as the look-back time of the KDC formation or older. Although the radii of our KDCs are on average larger than observed, we find that younger stellar ages are typically associated with smaller KDCs. A significant fraction of KDC hosts possess stellar shells formed during mergers that led to KDCs within the last 5 Gyr, or double peaks in their velocity dispersion maps.Comment: 18 pages, 16 figures, 1 table; accepted for publication in A&